Here, we reevaluated the “two-component” model of absolute pitch (AP) by combining behavioral and electrophysiological measurements. This specific model postulates that AP is driven by a perceptual encoding ability (i.e., pitch memory) plus an associative memory component (i.e., pitch labeling). To test these predictions, during EEG measurements AP and non-AP (NAP) musicians were passively exposed to piano tones (first component of the model) and additionally instructed to judge whether combinations of tones and labels were conceptually associated or not (second component of the model). Auditory-evoked N1/P2 potentials did not reveal differences between the two groups, thus indicating that AP is not necessarily driven by a differential pitch encoding ability at the processing level of the auditory cortex. Otherwise, AP musicians performed the conceptual association task with an order of magnitude better accuracy and shorter RTs than NAP musicians did, this result clearly pointing to distinctive conceptual associations in AP possessors. Most notably, this behavioral superiority was reflected by an increased N400 effect and accompanied by a subsequent late positive component, the latter not being distinguishable in NAP musicians.